Explore BrainMass

Explore BrainMass

    Real Analysis Topology and Sigma-Algebra

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    1). Prove that any sigma-algebra, which contains a finite number of members is also a topology. ( The Q in another words : to show that there exist a sequence of disjoint members of a sigma algebra which contains infinite no. of members).

    2). Does there exist an infinite sigma-algebra which has only countably many members? (Of course justify, examples, anything needed to prove any claims made in the solution.)

    © BrainMass Inc. brainmass.com March 4, 2021, 6:31 pm ad1c9bdddf
    https://brainmass.com/math/real-analysis/real-analysis-topology-sigma-algebra-48330

    Solution Preview

    1. Proof:
    We check the definition of sigma-algebra of topology. Suppose F is a sigma-algebra defined on the set X. We want to show that F is also a ...

    Solution Summary

    Sigma-algebras are investigated. The solution is detailed and well presented.

    $2.49

    ADVERTISEMENT